On the Mass Function of GWTC-2 Binary Black Hole Systems and Their Progenitors

The distribution of LIGO black hole binaries (BBH) shows an intermediate-mass range consistent with the Salpeter initial mass function (IMF) in black hole formation by core-collapse supernovae, subject to preserving binary association. They are effectively parameterized by the mean mass μ with a Pearson correlation coefficient of r = 0.93 ± 0.06 of secondary to primary masses with a mean mass ratio of q ¯ ≃ 0.67 , q = M 2 / M 1 , consistent with the paucity of intermediate-mass X-ray binaries. The mass function of LIGO BBHs is well approximated by a broken power law with a tail μ ≳ 31.4 M ⊙ in the mean binary mass μ = M 1 + M 2 / 2 . Its power-law index of α B , true = 4.77 ± 0.73 inferred from the tail of the observed mass function is found to approach the upper bound 2 α S = 4.7 of the uncorrelated binary IMF, defined by the Salpeter index α S = 2.35 of the IMF of stars. The observed low scatter in BBH mass ratio q evidences equalizing mass transfer in binary evolution prior to BBH formation. At the progenitor redshift z ′ , furthermore, the power-law index satisfies α B ′ > α B in a flat ΛCDM background cosmology. The bound α B , true ′ ≲ 2 α S hereby precludes early formation at arbitrarily high redshifts z ′ ≫ 1 , which may be made more precise and robust with extended BBH surveys from upcoming LIGO O4-5 observations.